Other Models

Too Many Rebels - The main flaw of all the more successful models is their overes-timation of the number of rebels. Whereas most estimates record the rebel army as between five thousand and fifteen thousand (Sydney Morning Herald, 1990; McCarthy, 1990; International Institute for Strategic Studies, 2008), most of the models show the rebels’ numbers to be around twenty-five thousand by the end of the period, with the lowest estimates (models A4.1 and B4.1) being about twenty thousand.

This leads to problems beyond just an overestimation in rebel strength. As all of the models assume the number of people killed is proportional to the sizes of the state’s army and the rebels’ forces, too many rebels equates with too many deaths, and thus the nearly universal overestimation among models of the final death toll.

One can imagine several possible explanations for this overestimation. The most

obvious is actually the easiest to correct (in theory, anyways): bad parameter values. If fR or iR is too big, or cR is too small, then clearly rebel troop counts will be too high.

Likewise, if kR is too large (not difficult to imagine, considering the necessarily hap-hazardous manner of its estimation), the hypothetical rebels will have more income to use for their hypothetical war effort than their living, breathing, and state-overthrowing counterparts. Unfortunately, the values of some of these numbers are known only to the rebels themselves, and thus may prove impervious to solid estimation.

Moving away from the conveniently easy explanation of deficient parameters, one can also examine possible structural defects in the models. One is the approximated opportunity cost assumption inherent in the termqiG

p - namely, that the cost of upkeep for a single rebel is the median income. Though this assumption deftly dodges the difficulty in calculating the actual rebel upkeep cost (again, something only the rebels themselves can know for sure), it could be utterly wrong. If so, then one would have to revert back to the level 1 rebel expense term xRR in all of the models, or at least find a more accurate proportion of GDP/capita to approximate rebel expenses.

The most difficult and unpleasant possibility is that the simplifying assumption that rebel training and outfitting can be accurately modeled by instantaneous inflows is wrong. If this is the case, one would have two options: either to create an additional population to represent rebels-in-training (thus losing some of the models’ simplicity), and have incoming rebels flow through this middle man term; or to use delay differential equations rather than ordinary differential equations (thus losing some of the analytic tools one has in studying ODEs). However, if one really cannot represent the training

of fighters as an instantaneous inflow, it seems logical that similar problems would arise in the state troop count. But as Table 5.1 makes clear, the size of the state’s forces is represented with shocking accuracy in all of the non-level 5 models.

Perpetual Recruitment - Another problem, more abstract because it creates prob-lems mainly over the long term, and yet potentially more dangerous because it leads to inaccuracies in qualitative behavior, is how both sides’ numbers increase indefinitely.

Though the rate at which both sides forces grow is very slight after their initial re-cruitment drives, it is nevertheless an upward trend. This is a problem because 1) as noted before, the amount of carnage predicted by the model increases with the number of combatants, so ever increasing combatant pools cause ever increasing death counts;

2) model analysis will be skewed because it assumes both sides are getting larger and larger over time.

Why do the models predict such swelling armies? Mainly because both sides receive some portion of their income from the GDP, which in the case of Sri Lanka has steadily grown despite the war. Thus, it makes sense that the state’s numbers are increasing faster than the rebels’, since the rebels rely primarily on foreign funding, which is as-sumed to stay constant in this model (though it might be worth changing this to reflect the growth of the GDPs of the countries from which their funds originate).

Why does an expanding GDP throw off the results like this? After all, the actual Sri Lankan military receives its income from taxes drawn from the GDP as well. And lest one think the reason is that the model does not take inflation into account, note thatr, the economic growth rate parameter, was calculated fromreal GDP growth rate

data rather than nominal data. In fact, the reason is probably that the model does not acknowledge that military technology, and thus military expenditure, expands over time much like the global economy. Thus, the ever increasing defense budget is invested in more advanced hardware rather than more soldiers, a trend that may well hold for the rebels as well as they throw down their homemade bazookas and pick up Stinger missiles instead.

Solving this problem would probably require a close study of changes in military technology and budget, something well beyond the scope of this study. However, it seems likely the the key to the problem lies in replacing the constants cS and cR with functions cS(t) and cR(t), thus making the system of ODEs non-autonomous. Perhaps something as simple ascS(t) =αt+c0, withα andc0 determined by fitting a trend line to past data on (inflation-adjusted) military hardware costs, would suffice.

Chapter 6

Model Analysis: Examining Apocalypse

Having painstakingly identifying the best model out of these sixteen, we can now extract some insight from it through some analysis. Before continuing, however, it would be useful to define some simple axioms to keep such insight relevant to the real world.

First, it seems reasonable to assume one is examining an actual inhabited country -in other words, as far as our purposes go, economic activity of some k-ind bounded by borders.

Axiom 1 (State Existence). G > 0 for all t.

It also seems reasonable to assume that neither side’s army will have a negative number of fighters, and also neither army can get too big as compared to the country’s population. In the case of Sri Lanka, if we let α denote the percent of the island’s

population made up of Tamil’s, which was roughly 18% in 1990 (Gamini and Chaudhary, 1990), and assume that neither side’s army is larger than 4% of its potential recruiting base, then we arrive at the following axiom:

Axiom 2 (Bounded Armies). 0≤S ≤ Smax =.04p and 0≤R ≤Rmax =.04αp for all t.

Note that this means 0 ≤ S ≤ 6.8454×10⁵ and 0 ≤ R ≤ 1.2322×10⁵, which is hardly too restrictive a bound (if both the army and the LTTE take their maximum values, then 4.72% of the population would be at war, a staggering number).

Finally, as all the parameters for all the models have implicit purposes and the use of addition and subtraction in their formulation follows those purposes(for example, fS

is meant as an inflow of foreign funds, d_RS1 is meant as a component in a kill rate), it seems reasonable to assume the parameters are non-negative to preserve the signs inherent to their purpose.

Axiom 3 (Parameter Non-Negativity). All parameters are non-negative real numbers.

6.1 Default d

, c

, d

, d

To start out, we make the simplifying assumption that the values ofd_C, c_C, d_RS and d_SR are those used to run the model in Chapter 5 (see Appendix B). With this assumption in place, several results arise through simple analysis.